The system of verse/chapter numbering that we take for granted today, was brand new in the 16th & 17th centuries, when the Douay (& KJV) were being translated. There was not yet an established rule as to how the system would work.
The Douay followed the traditional numbering of the Latin, which is somewhat different than that of the Jewish Bibles, from which we get our modern numbering.
If you check Psalm 9 in the Douay, you get to the 21st verse, & then there is a note saying that this is a chapter change in Hebrew Bibles. But what we would call verse 22, is numbered as verse 1…of the 10th Psalm.
What I have done is to simply write in the other numbering, to enhance the referencing of verses with other Bibles…It’s really only a minor pain, & I really do like the Douay Rheims very, very much, which makes it well worth it to go through & number things for myself.